Theory of Dimensionally Scaled Models of Petroleum Reservoirs

Abstract

Published in PetroleumTransactions, AIME, Volume 207, 1956, pages 118–127. Abstract The dimensionless groups, to which the variables that govern the displacement of oil from reservoirs by liquids can be combined, are derived. Three types of displacement are considered, viz. cold-water drive, hot-water drive and solvent injection. The derivation of the dimensionless groups is carried out by means of the relevant basic equations (inspectional analysis). The resulting sets of groups are afterwards completed by means of dimensional analysis. The form of the groups is given in such a way that they can be adapted to suit the various boundary conditions that are encountered in practice. The physical meaning of the groups is discussed. They have all been brought together on a chart, from which their mutual relation and their correspondence to related dimensionless groups in common use in other engineering sciences can be read off. The limitations of dimensionally scaled model experiments as a useful tool for studying liquid flow in porous media, as occurring in oil reservoirs, are discussed. " The use of models to study fluid mechanics has an appeal for everyone endowed with natural curiosity. What active boy has not played with ship and airplane models, or crude models of dam and drainage systems? Even in the most advanced technical engineering, such models play a fundamental and indispensable role. " And yet in few departments of the physical sciences is there a wider gap between theory and practice, between scientific knowledge and the state of art, than in the use of models to study hydrodynamic phenomena." Garrett Birkhoff Introduction Laboratory displacement experiments are extensively used to investigate, directly or indirectly, the production behavior of petroleum reservoirs. Such experiments are representative of the reservoirs as a whole, if they are carried out with models that are "properly scaled."